In my tests, chatgpt is not captured in the Referrer Type dimension as a Search Engine, but rather an Other Site.
When I asked my Technical Account Manager, they responded with the following:
"ChatGPT is not designed to be an SEO tool. It can provide information and suggestions based on web data, this information can sometimes be incorrect or misleading."
If you use Marketing Channels, you can customize what traffic gets assigned to Search Engines.